I am trying to share an aurora ticket and mystic ticket between my FR LG & E as well as an eon ticket between my RSE. I cannot find an option to send and I cant find any friends on the list for the cartridge that is receiving the gift
In Generation III, Mystery Gift is only available on Pokémon FireRed, LeafGreen, and Emerald by using a Game Boy Advance Wireless Adapter
-Bulbapedia
Mystery Gifts can be shared between FR/LG and E via the Wireless Adapter only.
Ruby and Sapphire share Mystery Gifts via a link cable.
Source: Bulbapedia